To study the shear characteristics of rubber–sand mixtures, the effects of four rubber–sand mixture gradations (one type of gap gradation, two types of continuous gradations, and one type of open gradation), three rubber contents (10%, 30%, and 60%), and three vertical stresses (30 kPa, 60 kPa, and 90 kPa) on the strength and volumetric change characteristics of rubber–sand mixtures were investigated by using a large-scale laboratory direct shear apparatus. Then, the discrete element models of pure sand and rubber–sand mixtures were established according to the same gradation and rubber content. The intrinsic mechanism of rubber–sand mixtures was explored from the perspective of particle contact state and displacement. The results show that the shear stress curve of rubber–sand mixtures is the same as that of pure sand at low rubber content, but its shear strength is lower than that of pure sand. The shear stress of rubber–sand mixtures increases with the increase in vertical stress, and the shear strength of continuous gradation SR2 is the largest among the four gradations of rubber–sand mixtures. The addition of rubber particles can effectively inhibit the dilatancy of sandy soil, among which the gap gradation SR1 has the best effect on inhibiting soil dilatancy, and the dilatancy is reduced by 37.6% compared with that of pure sand. The internal friction angle of rubber–sand mixtures decreases with the increase of rubber content, and the internal friction angle of continuous gradation SR2 is the largest under the same rubber content. Rubber particles mainly participate in the formation of weak force chain in the force chain network of rubber–sand mixtures, and the shear zone width of rubber–sand mixtures is smaller than that of pure sand.